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www.shapeoperator.com | ||
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micromath.wordpress.com
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| | | | | Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... | |
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jaydaigle.net
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| | | | | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. | |
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alexkritchevsky.com
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| | | | | [AI summary] The article critiques Geometric Algebra (GA) for its reliance on the geometric product, which the author finds problematic for most purposes. The author argues that GA's focus on complexifying vector algebra to resemble complex numbers and quaternions is unnecessary and confusing. Instead, the author advocates for a simpler approach using exterior algebra and wedge products, emphasizing clarity and intuition over abstract algebraic structures. The author also mentions the philosophical and pedagogical issues with GA, such as its conflation of operators and primitives, and the cultural baggage associated with the term 'Geometric Algebra.' The article concludes by suggesting that while GA has value as an implementation detail, it should not be see... | |
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kristalcantwell.wordpress.com
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| | | Mini-polymath 4 has started. It is based on question 3 of the IMO. The research thread is here. There is a wiki here. | ||
